Certain problems in the theory of fractional-order linear differential operators
type: Item
instance of: scholarly article
title: Certain problems in the theory of fractional-order linear differential operators
zbMATH Open document ID: 0886.34008
author: O. Diekmann
published in: Doklady Mathematics
publication date: 1998-05-04T00:00:00Z
review text: A transformation operator is constructed which replaces the solution of the equation \[ D_{0x}^{(\sigma)}u- \{\lambda+q(x)\}u=0 \tag{1} \] with the solution of \[ D_{0x}^{(\sigma)}u- \lambda u=0.\tag{2} \] Here \(D_{0x}^{(\sigma)}\) is an operator of fractional (in the Riemann-Liouville sense) differentiation of order \(1<\sigma\leq 2\). A function which solves a problem \[ D_{0x}^{(\sigma-2)} u|_{x=0}= h_0, \qquad D_{0x}^{(\sigma-1)} u|_{x=0}= h_1 \] for equation (1) is constructed with the aid of a solution of equation (2). Properties of the fractional operator are discussed.
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 1050607
zbMATH Keywords: single-cell operator
zbMATH Keywords: fractional operator
zbMATH Keywords: transformation operator
reviewed by: Josef Diblík
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1050607